Multiplication of Single Digits

Multiplication is just repeated addition, and once you get comfortable with single-digit multiplication (the times tables), everything from multi-digit multiplication to algebra gets easier.

$3 \times 4$ means “3 groups of 4” or equivalently “add 4 three times”:

$$3 \times 4 = 4 + 4 + 4 = 12$$

The $\times$ sign means “groups of.” You can also read it as “times.”

Key ideas:

• Order doesn’t matter: $3 \times 4 = 4 \times 3 = 12$
• Multiplying by 1 changes nothing: $7 \times 1 = 7$
• Multiplying by 0 always gives 0: $5 \times 0 = 0$

Here’s the complete table. The green diagonal shows the perfect squares (a number times itself). Use this as a reference until the facts become second nature.

×	1	2	3	4	5	6	7	8	9	10	11	12
1	1	2	3	4	5	6	7	8	9	10	11	12
2	2	4	6	8	10	12	14	16	18	20	22	24
3	3	6	9	12	15	18	21	24	27	30	33	36
4	4	8	12	16	20	24	28	32	36	40	44	48
5	5	10	15	20	25	30	35	40	45	50	55	60
6	6	12	18	24	30	36	42	48	54	60	66	72
7	7	14	21	28	35	42	49	56	63	70	77	84
8	8	16	24	32	40	48	56	64	72	80	88	96
9	9	18	27	36	45	54	63	72	81	90	99	108
10	10	20	30	40	50	60	70	80	90	100	110	120
11	11	22	33	44	55	66	77	88	99	110	121	132
12	12	24	36	48	60	72	84	96	108	120	132	144

Notice the table is symmetric across the diagonal: $3 \times 7$ and $7 \times 3$ are both 21. That cuts the number of facts you need to memorize roughly in half.

$2 \times$ anything is the same as adding the number to itself:

• $2 \times 3 = 6$ (double 3)
• $2 \times 7 = 14$ (double 7)
• $2 \times 9 = 18$ (double 9)

Results always end in 0 or 5:

• $5 \times 1 = 5$
• $5 \times 2 = 10$
• $5 \times 3 = 15$
• $5 \times 4 = 20$

The digits of any 9s product always add up to 9:

• $9 \times 2 = 18$ (1 + 8 = 9)
• $9 \times 3 = 27$ (2 + 7 = 9)
• $9 \times 4 = 36$ (3 + 6 = 9)
• $9 \times 7 = 63$ (6 + 3 = 9)

Also: the tens digit is always one less than what you’re multiplying by. $9 \times 7$: tens digit is 6, ones digit is 3 (since 6 + 3 = 9). Answer: 63.

• $10 \times 3 = 30$
• $10 \times 7 = 70$

These come up constantly:

• $1 \times 1 = 1$
• $2 \times 2 = 4$
• $3 \times 3 = 9$
• $4 \times 4 = 16$
• $5 \times 5 = 25$
• $6 \times 6 = 36$
• $7 \times 7 = 49$
• $8 \times 8 = 64$
• $9 \times 9 = 81$

Most people find these the hardest to memorize:

• $6 \times 7 = 42$
• $6 \times 8 = 48$
• $7 \times 8 = 56$
• $8 \times 9 = 72$

A trick for $7 \times 8$: “5, 6, 7, 8” → $56 = 7 \times 8$.

$6 \times 9$

Use the 9s trick: tens digit = 5 (one less than 6), ones digit = 4 (since 5 + 4 = 9). Answer: 54.

$8 \times 7$

If you know $7 \times 7 = 49$, then $8 \times 7 = 49 + 7 = 56$.

$4 \times 8$

Double 8 twice: $2 \times 8 = 16$, then $2 \times 16 = 32$. So $4 \times 8 = 32$.